Finite Group Databasebeta

← C5×C31×(C3⋊D3)⋊D5 #42124930

Subgroups — C5×C31×(C3⋊D3)⋊D5 #42124930

Order 27900.

224 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×D15×C31C212yesmaximal, complemented
2C52×C3⋊D3×C31C211yesmaximal, characteristic, complemented
3C5×D3×D5×C31—32nomaximal
4C32×C52×C31C2211yescharacteristic, complemented, Hall
5C31×(C3⋊D3)⋊D5C511yesmaximal, characteristic, direct product factor
6C5×D32×C31—51nomaximal
7C5×D15×C31D312yescomplemented
8C52×D3×C31—32no—
9C52×D3×C31—61no—
10C3×C5×D5×C31—32no—
11C2×C5×D5×C31—91noHall
12C5×C3⋊D3×C31—22no—
13C5×C3⋊D3×C31D511yescharacteristic, complemented
14C5×C3⋊D3×C31C2×C511yescharacteristic, complemented
15C3×D15×C31C2×C512yescomplemented
16C3×C5×D3×C31—52no—
17C3×C52×C31—21no—
18C3×C52×C31C2×D312yescomplemented
19C2×C5×D3×C31—152no—
20D3×D5×C31—32no—
21C2×C52×C31—91no—
22C5×D5×C31—32no—
23C32×C5×C31—22no—
24C32×C5×C31C2×D511yescharacteristic, complemented
25C32×C5×C31C22×C511yescharacteristic, complemented
26D32×C31—51noHall
27C2×C3×C5×C31—152no—
28D15×C31C5×D312yescomplemented
29C5×D3×C31—32no—
30C5×D3×C31—32no—
31C5×D3×C31—52no—
32C5×D3×C31—64no—
33C5×D3×C31—61no—
34C5×D3×C31—61no—
35C5×D3×C31—64no—
36C3×D5×C31—32no—
37C5×(C3⋊D3)⋊D5C3111yesmaximal, characteristic, direct product factor, Hall
38C52×C31D3211yescharacteristic, complemented, Hall
39C22×C5×C31—451no—
40C2×D5×C31—91no—
41C3⋊D3×C31C5×D511yescharacteristic, complemented
42C3×D3×C31—52no—
43C3×C5×C31—24no—
44C3×C5×C31—21no—
45C3×C5×C31—21no—
46C3×C5×C31—24no—
47C3×C5×C31D3×D512yescomplemented
48C3×C5×C31C2×C5×D312yescomplemented
49C52×C3⋊D3C2×C3111yescharacteristic, complemented
50C3×C5×D15C2×C3112yescomplemented
51C2×D3×C31—152no—
52C2×C5×C31—91no—
53C2×C5×C31—91no—
54C2×C5×C31—152no—
55C2×C5×C31—182no—
56D5×C31—32no—
57C5×D3×D5—32no—
58C32×C31C2×C5×D511yescharacteristic, complemented, Hall
59C32×C52C22×C3111yescharacteristic, complemented, Hall
60C2×C3×C31—152no—
61D3×C31—32no—
62D3×C31—52no—
63D3×C31—61no—
64(C3⋊D3)⋊D5C5×C3111yescharacteristic, direct product factor
65C5×D32—51no—
66C5×C31—22no—
67C5×C31C5×D3211yescharacteristic, complemented
68C5×C31(C3⋊D3)⋊D511yescharacteristic, direct product factor
69C5×D15D3×C3112yescomplemented
70C52×D3—32no—
71C52×D3—61no—
72C3×C5×D5—32no—
73C22×C31—451noHall
74C2×C5×D5—91noHall
75C3×C31—21no—
76C3×C31C5×D3×D512yescomplemented
77C5×C3⋊D3—22no—
78C5×C3⋊D3D5×C3111yescharacteristic, complemented
79C5×C3⋊D3C2×C5×C3111yescharacteristic, complemented
80C3×D15C2×C5×C3112yescomplemented
81C3×C5×D3—52no—
82C3×C52—21no—
83C3×C52C2×D3×C3112yescomplemented
84C2×C31—91no—
85C2×C31—152no—
86C2×C5×D3—152no—
87D3×D5—32no—
88C2×C52—91no—
89C5×D5—32no—
90C32×C5—22no—
91C32×C5C2×D5×C3111yescharacteristic, complemented
92C32×C5C22×C5×C3111yescharacteristic, complemented
93D32—51noHall
94C31C5×(C3⋊D3)⋊D511yescharacteristic, direct product factor, Sylow
95C2×C3×C5—152no—
96D15C5×D3×C3112yescomplemented
97C3×D5—32no—
98C5×D3—32no—
99C5×D3—32no—
100C5×D3—52no—
101C5×D3—64no—
102C5×D3—61no—
103C5×D3—61no—
104C5×D3—64no—
105C52D32×C3111yescharacteristic, complemented, Sylow
106C22×C5—451no—
107C2×D5—91no—
108C3⋊D3C5×D5×C3111yescharacteristic, complemented
109C3×D3—52no—
110C3×C5—24no—
111C3×C5—21no—
112C3×C5—21no—
113C3×C5—24no—
114C3×C5D3×D5×C3112yescomplemented
115C3×C5C2×C5×D3×C3112yescomplemented
116C2×D3—152no—
117C2×C5—91no—
118C2×C5—91no—
119C2×C5—152no—
120C2×C5—182no—
121D5—32no—
122C32C2×C5×D5×C3111yescharacteristic, complemented, Sylow
123C2×C3—152no—
124D3—32no—
125D3—52no—
126D3—61no—
127C5—22no—
128C5C5×D32×C3111yescharacteristic, complemented
129C5C31×(C3⋊D3)⋊D511yescharacteristic, direct product factor
130C22—451noSylow
131C3—21no—
132C3C5×D3×D5×C3112yescomplemented
133C2—91no—
134C2—152no—
subgroupG/H
center, hypercenterC5×C31(C3⋊D3)⋊D5
commutator, cosocle, hypocenterC32×C5C22×C5×C31
FrattiniC1G
Fitting, socleC32×C52×C31C22
LCSG ▷ C32×C5
UCSC1 ◁ C5×C31

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×C5×D15×C31C2semidirect
2. C52×C3⋊D3×C31C2semidirect
4. C32×C52×C31C22semidirect
5. C31×(C3⋊D3)⋊D5C5direct (N × H)
7. C5×D15×C31D3semidirect
13. C5×C3⋊D3×C31D5semidirect
14. C5×C3⋊D3×C31C2×C5semidirect
15. C3×D15×C31C2×C5semidirect
18. C3×C52×C31C2×D3semidirect
24. C32×C5×C31C2×D5semidirect
25. C32×C5×C31C22×C5semidirect
28. D15×C31C5×D3semidirect
37. C5×(C3⋊D3)⋊D5C31direct (N × H)
38. C52×C31D32semidirect
41. C3⋊D3×C31C5×D5semidirect
47. C3×C5×C31D3×D5semidirect
48. C3×C5×C31C2×C5×D3semidirect
49. C52×C3⋊D3C2×C31semidirect
50. C3×C5×D15C2×C31semidirect
58. C32×C31C2×C5×D5semidirect
59. C32×C52C22×C31semidirect
64. (C3⋊D3)⋊D5C5×C31direct (N × H)
67. C5×C31C5×D32semidirect
68. C5×C31(C3⋊D3)⋊D5direct (N × H)
69. C5×D15D3×C31semidirect
76. C3×C31C5×D3×D5semidirect
78. C5×C3⋊D3D5×C31semidirect
79. C5×C3⋊D3C2×C5×C31semidirect
80. C3×D15C2×C5×C31semidirect
83. C3×C52C2×D3×C31semidirect
91. C32×C5C2×D5×C31semidirect
92. C32×C5C22×C5×C31semidirect
94. C31C5×(C3⋊D3)⋊D5direct (N × H)
96. D15C5×D3×C31semidirect
105. C52D32×C31semidirect
108. C3⋊D3C5×D5×C31semidirect
114. C3×C5D3×D5×C31semidirect
115. C3×C5C2×C5×D3×C31semidirect
122. C32C2×C5×D5×C31semidirect
128. C5C5×D32×C31semidirect
129. C5C31×(C3⋊D3)⋊D5direct (N × H)
132. C3C5×D3×D5×C31semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×C5×D15×C312
C52×C3⋊D3×C312
C5×D3×D5×C313
C31×(C3⋊D3)⋊D55
C5×D32×C315
C5×(C3⋊D3)⋊D531